How do I convert 2,000 from decimal to hexadecimal?

It helps if you think of the columns in your hexadecimal number as powers of 16, so your first digit will represent how many lots of \(\displaystyle \displaystyle \begin{align*} 16^0 \end{align*}\), the second digit will represent how many lots of \(\displaystyle \displaystyle \begin{align*} 16^1 \end{align*}\), the third digit will represent how many lots of \(\displaystyle \displaystyle \begin{align*} 16^2 \end{align*}\), etc. Notice that \(\displaystyle \displaystyle \begin{align*} 16^2 = 256 \end{align*}\) and \(\displaystyle \displaystyle \begin{align*} 16^3 = 4069 \end{align*}\), so that means in hexadecimal your number can only have three digits.

Now notice that \(\displaystyle \displaystyle \begin{align*} \frac{2000}{16^2} = 7\,\frac{208}{16^2} \end{align*}\), so your \(\displaystyle \displaystyle \begin{align*} 16^2 \end{align*}\) digit is \(\displaystyle \displaystyle \begin{align*} 7 \end{align*}\). You are left with \(\displaystyle \displaystyle \begin{align*} 208 \end{align*}\).

Now notice that \(\displaystyle \displaystyle \begin{align*} \frac{208}{16} = 13 \end{align*}\), so your \(\displaystyle \displaystyle \begin{align*} 16^1 \end{align*}\) digit will have to be a \(\displaystyle \displaystyle \begin{align*} d \end{align*}\) (which is the 13th digit).

Since there is no remainder, your \(\displaystyle \displaystyle \begin{align*} 16^0 \end{align*}\) term has to be \(\displaystyle \displaystyle \begin{align*} 0 \end{align*}\).

Therefore \(\displaystyle \displaystyle \begin{align*} 2000_{10} = 7d0_{16} \end{align*}\).